4 papers · 1 filter
A noise-induced transition in the Lorenz system
Michele Coti Zelati, Martin Hairer
We consider a stochastic perturbation of the classical Lorenz system in the range of parameters for which the origin is the global attractor. We show that adding noise in the last…
Fluctuations of stochastic PDEs with long-range correlations
Luca Gerolla, Martin Hairer, Xue-Mei Li
We study the large-scale dynamics of the solution to a nonlinear stochastic heat equation (SHE) in dimensions with long-range dependence. This equation is driven by mult…
Stochastic quantisation of Yang-Mills-Higgs in 3D
Ajay Chandra, Ilya Chevyrev, Martin Hairer +1
We define a state space and a Markov process associated to the stochastic quantisation equation of Yang-Mills-Higgs (YMH) theories. The state space is a nonlinear met…
Discretisation of regularity structures
Dirk Erhard, Martin Hairer
We introduce a general framework allowing to apply the theory of regularity structures to discretisations of stochastic PDEs. The approach pursued in this article is that we do not…